Final answer:
The solution to the linear inequality is solved by first isolating x, then finding the upper bound of the inequality. The correct missing value which completes the inequality -8 ≤ 3x + 6 is -4. So, the solution in interval notation is [-14/3, -10/3].
Step-by-step explanation:
To solve the linear inequality and express the solution using interval notation, first we need to isolate the variable x. The inequality given is -8 ≤ 3x + 6. We can subtract 6 from all parts of the inequality to get -14 ≤ 3x. Then we divide each part by 3 to solve for x and get -14/3 ≤ x, or x ≥ -14/3.
The inequality must hold for both ends, so we need to find the missing value that completes the second part of the inequality, which is already given by the options provided.
Therefore, the complete inequality should be -8 ≤ 3x + 6 ≤ -4. Following the previous steps, subtracting 6 from all parts and then dividing by 3: (-8 - 6)/3 ≤ x ≤ (-4 - 6)/3. Simplifying, we get -14/3 ≤ x ≤ -10/3.
Therefore, in interval notation, the solution is [-14/3, -10/3]. Hence, the correct missing value in the original inequality is -4, which is option d.